take warning from, learn from, pattern, example
鑒 centers on using a reflective surface to examine oneself or a situation: taking warning from past events, learning from an example, or holding something up as a pattern to follow.
鑒 is a variant form of 鑑, combining 金 (metal) with a component related to looking or reflecting. The character originally referred to a metal mirror used for self-examination, which extended to the idea of taking warning or learning from an example.
Picture a polished metal (金) mirror held up to examine yourself. The reflection shows your past mistakes, warning you to learn and follow a better pattern.
For カン, imagine a can of polish used to shine the metal mirror: can -> カン, and the shiny surface lets you see your reflection clearly.
the gods watching over humans from the heavens